the starter motor earths to the engine case,its thick black wire goes to one side of a solenoid,,the other terminal of the solenoid goes to the battery positive,,the two small wires out of the solenoid are for the starter button,,power goes to one via the key switch,then the start button earths out the other and the solenoid operates,this can also be visa versa,the solenoid is just a big heavy duty relay switch,it connects the starter cable to the battery positive so long as you hold the button.,,you have missing/modified wiring?have you got a local buddy who can help?
if you touch that starter black wire to the battery itll spin the starter so long as its body is earthed,you might try jumping it with starter cables.